Three-Dimensional Space Interpolation of Grey / Depth Image Sequence-A New Technique of Computer Graphics Synthesis

This paper advances a three-dimensional space interpolation method of grey / depth image sequence, which breaks free from the limit of original practical photographing route. Pictures can cruise at will in space. By using space sparse sampling, great memorial capacity can be saved and reproduced scenes can be controlled. To solve time consuming and complex computations in three-dimensional interpolation algorithm, we have studied a fast and practical algorithm of scattered space lattice and that of 'Warp' algorithm with proper depth. By several simple aspects of three dimensional space interpolation, we succeed in developing some simple and practical algorithms. Some results of simulated experiments with computers have shown that the new method is absolutely feasible.

INTERPOLATION SPACES BETWEEN H^1 AND L~∞ ON SPACES OF HOMOGENEOUS TYPE

Using the maximal function characterization of Hardy spaces, we study the interpolation spaces between H1 and L∞ on spaces of homogeneous type.

Real Interpolation Between B-valued Martingale Hardy Spaces

The interpolation spaces between Banach space valued martingale Hardy spaces, between Hardy and BMO spaces are identified respectively. Some results obtained here are connected closely with the convexity and smoothness of the Banach space which the martingales take values in.

ON BEST INTERPOLATION IN ORLICZ SPACES

For given data,an interpotant is sought,so that a cerlaint convcx functional de fined bv a Young's function in the corresponding Orlicz space is minuimized.The feedciainmore general kind of spaces can be used for selecting the interpolunts in an udequare class of functiois.

APPROXIMATION ORDER AND INTERPOLATION SPACES

In this paper we introduce the two-parameter operators on Abelian group and establish their interpolation theorems of approximation, which are extensions of the interpolation theorems for nonlinear best approximation by R. Devore and are suitable for the approximation of oprators.

DIRECT AND INVERSE THEOREMS FOR JACKSON MEANS OF ENTIRE EXPONENTIAL TYPE IN B_α SPACES

This paper presents a new type of interpolation of Bα spaces,with which a new characterization of Bα spaces by the Jackson means of entire exponential type is given.

Interpolation Spaces between L^1 and BMO on Spaces of Homogeneous Type

We study the interpolation spaces between L^1 and BMO on spaces of homogeneous type. For 0 〈 θ 〈 1, 1≤q ≤∞, we obtain （L^1,BMO）θ,q =Lpq, where θ=1-1/p.

EXISTENCE AND STABILITY OF PERIODIC AND ALMOST PERIODIC SOLUTIONS TO THE BOUSSINESQ SYSTEM IN UNBOUNDED DOMAINS

In this paper we investigate the existence and stability of periodic solutions(on a half-line R_(+))and almost periodic solutions on the whole line time-axis R to the Boussinesq system on several classes of unbounded domains of R^(n) in the framework of interpolation spaces.For the linear Boussinesq system we combine the L^(p)—L^(q)-smoothing estimates and interpolation functors to prove the existence of bounded mild solutions.Then,we prove the existence of periodic solutions by invoking Massera’s principle.We also prove the existence of almost periodic solutions.Then we use the results of the linear Boussinesq system to establish the existence,uniqueness and stability of the small periodic and almost periodic solutions to the Boussinesq system using fixed point arguments and interpolation spaces.Our results cover and extend the previous ones obtained in[13,34,38].

ABSTRACT CAPACITY OF REGIONS AND COMPACT EMBEDDING WITH APPLICATIONS

The weighted Sobolev-Lions type spaces W pl,γ（Ω; E0, E） = W pl,γ（Ω; E） ∩ Lp,γ （Ω; E0） are studied, where E0, E are two Banach spaces and E0 is continuously and densely embedded on E. A new concept of capacity of region Ω ∈ Rn in W pl,γ（; E0, E） is introduced. Several conditions in terms of capacity of region Ω and interpolations of E0 and E are found such that ensure the continuity and compactness of embedding operators. In particular, the most regular class of interpolation spaces Eα between E0 and E, depending of α and l, are found such that mixed differential operators Dα are bounded and compact from W pl,γ（Ω; E0, E） to Eα-valued Lp,γ spaces. In applications, the maximal regularity for differential-operator equations with parameters are studied.

Interpolated Tensor Products of Exponential Type Vectors of Unbounded Operators

In this paper we define the tensor products of spaces of exponential type vectors of closed unbounded operators in Banach spaces. Using the real method of interpolation （K-functional） we prove the interpolation theorems that permit to characterize of tensor products of spaces of exponential type vectors, We show an application of abstract results to the theory of regular elliptic operators on bounded domains. For such operators the exponential type vectors are root vectors. Thus we describe the tensor products of root vectors of regular elliptic operators on bounded domains.

Embedding and Maximal Regular Differential Operators in Sobolev-Lions Spaces

This study focuses on vector-valued anisotropic Sobolev-Lions spaces associated with Banach spaces E0, E. Several conditions are found that ensure the continuity and compactness of embedding operators that are optimal regular in these spaces in terms of interpolations of spaces E0 and E. In particular, the most regular class of interpolation spaces Eα between E0, E depending on α and the order of space are found and the boundedness of differential operators D^α from this space to Eα-valued Lp,γ spaces is proved. These results are applied to partial differential-operator equations with parameters to obtain conditions that guarantee the maximal Lp,γ regularity and R-positivity uniformly with respect to these parameters.

Embedding Theorems in J5-Spaces and Applications

This study focuses on the anisotropic Besov-Lions type spaces B^lp,θ（Ω;E0,E） associated with Banach spaces E0 and E. Under certain conditions, depending on l =（l1,l2,…,ln）and α=（α1,α2,…,αn）,the most regular class of interpolation space Eα between E0 and E are found so that the mixed differential operators D^α are bounded and compact, from B^l＋s p,θ（Ω;E0,E） to B^s p,θ（Ω;Eα）.These results are applied to concrete vector-valued function spaces and to anisotropic differential-operator equations with parameters to obtain conditions that guarantee the uniform B separability with respect to these parameters. By these results the maximal B-regularity for parabolic Cauchy problem is obtained. These results are also applied to infinite systems of the quasi-elliptic partial differential equations and parabolic Cauchy problems with parameters to obtain sufficient conditions that ensure the same properties.

Absolutely Summing Multipliers on Abstract Hardy Spaces

We study summing multipliers from Banach spaces of analytic functions on the unit disc of the complex plane to the complex Banach sequence lattices. The domain spaces are abstract variants of the classical Hardy spaces generated by the complex symmetric spaces. Applying interpolation methods, we prove the Hausdorff Young and Hardy-Littlewood type theorems. We show applications of these results to study summing multipliers from the Hardy-Orlicz spaces to the Orlicz sequence lattices. The obtained results extend the well-known results for the Hp spaces.

A new grid deformation technology with high quality and robustness based on quaternion

Quality and robustness of grid deformation is of the most importance in the field of aircraft design, and grid in high quality is essential for improving the precision of numerical simulation. In order to maintain the orthogonality of deformed grid, the displacement of grid points is divided into rotational and translational parts in this paper, and inverse distance weighted interpolation is used to transfer the changing location from boundary grid to the spatial grid. Moreover, the deformation of rotational part is implemented in combination with the exponential space mapping that improves the certainty and stability of quaternion interpolation. Furthermore, the new grid deformation technique named ‘‘layering blend deformation＇＇ is built based on the basic quaternion technique, which combines the layering arithmetic with transfinite interpolation（TFI） technique. Then the proposed technique is applied in the movement of airfoil, parametric modeling, and the deformation of complex configuration, in which the robustness of grid quality is tested. The results show that the new method has the capacity to deal with the problems with large deformation, and the ‘‘layering blend deformation＇＇ improves the efficiency and quality of the basic quaternion deformation method significantly.

Well-Posedness of Equations with Fractional Derivative via the Method of Sum

We study the well-posedness of the equations with fractional derivative D^αu（t）= Au（t） ＋ f（t） （0 ≤ t ≤ 2π）, where A is a closed operator in a Banach space X, 0 〈 α 〈 1 and D^αis the fractional derivative in the sense of Weyl. Although this problem is not always well-posed in L^P（0, 2π; X） or periodic continuous function spaces Cper（[0, 2π]; X）, we show by using the method of sum that it is well-posed in some subspaces of L^P（0, 2π; X） or Cper （[0, 2π]; X）.

Abstract Elliptic Equations with Integral Boundary Conditons

This paper focuses on nonlocal integral boundary value problems for elliptic differential-operator equations. Here given conditions guarantee that maximal regularity and Fredholmness in L_p spaces. These results are applied to the Cauchy problem for abstract parabolic equations, its infinite systems and boundary value problems for anisotropic partial differential equations in mixed L_p norm.

Carleman estimates and unique continuation property for the anisotropic differential-operator equations

The unique continuation theorems for the anisotropic partial differential-operator equations with variable coefficients in Banach-valued L p -spaces are studied. To obtain the uniform maximal regularity and the Carleman type estimates for parameter depended differential-operator equations, the sufficient conditions are founded. By using these facts, the unique continuation properties are established. In the application part, the unique continuation properties and Carleman estimates for finite or infinite systems of quasielliptic partial differential equations are studied.

INTERIOR SUPERCONVERGENCE ERRORESTIMATES FOR MIXED FINITEELEMENT METHODS FOR SECOND ORDER ELLIPTIC PROBLEM

The aim of this paper is to provide a local superconvergence analysis for ined finite element methods of Poission equation. We shall prove that if p is smmoth enough in a local regionΩ0Ω1Ω and rectangular mesh is imposed onΩ1, then local superconvergence for are expected. Thus, by post-processing operators P and we have obtained the follwing local superconvergence error estimate: